$f({\sf R})$ Gravity Wormholes sourced by a Phantom Scalar Field

TL;DR

This paper derives exact wormhole solutions in $f(R)$ gravity supported by a phantom scalar field, demonstrating models free of ghosts and tachyonic instabilities without specifying the $f(R)$ function.

Contribution

It provides a novel class of wormhole solutions in $f(R)$ gravity supported by a self-interacting phantom scalar field, avoiding common instabilities.

Findings

Wormhole solutions supported by a phantom scalar field in $f(R)$ gravity.

The models are free of ghosts and tachyonic instabilities.

The $f(R)$ function is not explicitly specified, but the solutions are consistent and stable.

Abstract

We derive an exact wormhole spacetime supported by a phantom scalar field in the context of $f({\sf R})$ gravity. Without specifying the form of the $f({\sf R})$ function, the scalar field self-interacts with a mass term potential that is derived from the scalar equation and the resulting $f({\sf R})$ model is purely supported by the scalar field and it is free of ghosts and avoids the tachyonic instability.